Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneElementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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Page 74
... polygon of 2n sides is 2 ( 1 − 1 ) right angles . - 5. If the angle of a trammel is 60 ° what arc of a circle will it describe ? what if its angle is n ° ? 6. Trisect a right angle and thence show how to draw a regular 12 - sided polygon ...
... polygon of 2n sides is 2 ( 1 − 1 ) right angles . - 5. If the angle of a trammel is 60 ° what arc of a circle will it describe ? what if its angle is n ° ? 6. Trisect a right angle and thence show how to draw a regular 12 - sided polygon ...
Page 86
... REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in general called a polygon . They are named according to the number of their sides as follows : - 3 , triangle or trigon ; 4 ...
... REGULAR POLYGONS . 132 ° . Def . I. A closed rectilinear figure without re - entrant angles ( 89 ° , 2 ) is in general called a polygon . They are named according to the number of their sides as follows : - 3 , triangle or trigon ; 4 ...
Page 87
Nathan Fellowes Dupuis. regular polygon , the magnitude of an internal angle is ( 2-4 ) right angles . 11 . Proof . - Let AB , BC be two consecu- tive sides of the polygon and O its centre . Then the triangles AOB , BOC are isosceles and ...
Nathan Fellowes Dupuis. regular polygon , the magnitude of an internal angle is ( 2-4 ) right angles . 11 . Proof . - Let AB , BC be two consecu- tive sides of the polygon and O its centre . Then the triangles AOB , BOC are isosceles and ...
Page 88
... regular hexagon . Cor . Since AOB is an equilateral triangle , AB = AO ... polygon of any species may be capable of filling the plane , the number of ... regular polygons which can fill the plane , the hexagon includes the greatest area ...
... regular hexagon . Cor . Since AOB is an equilateral triangle , AB = AO ... polygon of any species may be capable of filling the plane , the number of ... regular polygons which can fill the plane , the hexagon includes the greatest area ...
Page 99
... polygon is regular every side is at the same distance from the centre . This distance is the apothem of the polygon . Thus if ABCD ... LA be a regu- lar polygon and O the centre ( 132 ° , Def . 2 ) , the triangles OAB , овс , are all ...
... polygon is regular every side is at the same distance from the centre . This distance is the apothem of the polygon . Thus if ABCD ... LA be a regu- lar polygon and O the centre ( 132 ° , Def . 2 ) , the triangles OAB , овс , are all ...
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Common terms and phrases
A. W. VERRALL ABCD algebraic altitude Assistant Master bisects BOOK Cambridge centre of similitude centre-line circles touch circumcircle co-axal coincide collinear common concurrent concurrent lines concyclic congruent cuts denote diagonals diameter divided Edited ELEMENTARY end-points equal angles equianharmonic equilateral triangle excircles EXERCISES external bisector FASNACHT Fcap fixed point G. E. FASNACHT geometric given circles given line given point GREEK harmonic range Hence HISTORY homographic Illustrated inverse points ISAAC TODHUNTER isosceles LAOB line-segment LL.D Mathematical median middle point orthogonally Owens College pair parallel parallelogram passes pencil perpendicular plane point of contact point of intersection Prof Professor Proof quadrangle radical axis radii radius rectangle regular polygon respect revised right angle right bisector rotation School secant Similarly square straight angle symbol tangent theorem Theorem.-The three circles Translated Trinity College vertex vertices
Popular passages
Page 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
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References to this book
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore No preview available - 2008 |
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore No preview available - 2008 |